Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2013 · Mathematics · Indefinite Integration

What is ∫ e^ e^x e^x d x equal to? where c is an arbitrary constant.

What is ∫eexexdx\int e^{e^x} e^x d x equal to? where c is an arbitrary constant.

Options

  1. Aeex+ce^{e^x}+c
  2. B2eex+c2 e^{e^x}+c
  3. Ceexex+ce^{e^x} e^x+c
  4. D2eexex+c2 e^{e^x} e^x+c

Correct answer

A. eex+ce^{e^x}+c

Step-by-step solution

I=∫eex⋅ex⋅dx\mathrm{I}=\int e^{e^x} \cdot e^x \cdot d x Let eex=y\quad e^{e^x}=y then, ex=ln⁡(y)\quad e^x=\ln (y) and, ex⋅dx=1y⋅dy\quad e^x \cdot d x=\frac{1}{y} \cdot d yI=∫y⋅1y⋅dy=∫dy=y+c=eex+c\begin{aligned} \mathrm{I} & =\int y \cdot \frac{1}{y} \cdot d y \\ & =\int d y=y+c \\ & =e^{e^x}+c \end{aligned}$$
Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value… NDA 2026Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value… NDA 2026What is ∫ dx 10^x + 10^ -x equal to? NDA 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)^… NDA 2025For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . Consider… NDA 2025For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . What is u +… NDA 2025Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of β ? NDA 2024Paragraph: Let 2 ∫ x^2-1 x^2+1 d x=U(x) V(x)-3 \ U(x)+V(x)\ +c Question: What is U(x)… NDA 2024Paragraph: Let 2 ∫ x^2-1 x^2+1 d x=U(x) V(x)-3 \ U(x)+V(x)\ +c Question: What is… NDA 2024Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of… NDA 2024Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of… NDA 2024Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of α ? NDA 2024Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further… NDA 2023Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further… NDA 2023What is ∫(x^x)^2(1+ x) d x equal to? NDA 2022What is ∫ e^ x (1+ x+x x) d x equal to? NDA 2022 Full Indefinite Integration list Indefinite Integration JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs